Alright, I know this idea has been put forth a few times, but I just got an idea how it could be balanced; it wouldn't give people the ability to totally break the game or overpower newish players, but still give a reason to use up favor points after you've bought your preferred items.
Instead of making favor items from scratch, give the ability to upgrade them in spesific ways, like you level up demigods. And like demigods, there'd be a cap, so you couldn't max out everything, and have to make choices, pay more favor points to change your mind and put stats in other areas.
For example, Blood Vial gives hp and hp regen. You could put points to buff either, or like demigods have general skills, put points into some general, universial abilities; a shorter cooldown for usable items, a bit of an armor or attack speed boost, ect.
Of course, since there's a lot of items and they have rather spesific uses, there would be less abilities to choose from and less points to spend than with demigods. Also, the favor items might need a minor nerf to their 'base' stats to start with, to keep them in balance.